The authors welcome comment on the method and results contained in this draft paper. Comments should be sent to Shahidullah by July 2000, email shahidullah@abs.gov.au. Following feedback, ABS proposes publishing 1995-97 experimental life tables in Deaths, 1999 (ABS Cat. No. 3302.0).

The life expectancy estimates presented in this paper are described as experimental because of the nature of the base population, which is affected by the intercensal volatility in the counts of the Indigenous population, and deficiencies in deaths and births registration data. Consequently, there is uncertainty about the accuracy of death rates which use census counts or census-based population estimates as their denominator. The life expectancy estimates are therefore sensitive to the inputs used and over-precise analysis is cautioned. They should be used only as an indicative summary measure of the level of mortality of the Indigenous population.

The standard approach to calculating death rates is based on applying the number of deaths in a given period to the 'exposed to risk' population during that period. Without accurate data on Aboriginal and Torres Strait Islander (Indigenous) births and deaths, and accurate data on the size and structureof the Indigenous population, the standard method for calculating Indigenousdeath rates cannot be used.

A demographic technique outlined by Preston and Hill was used to estimate the completeness of Indigenous death registration. Based on the analysis presented here, 39.1% of Indigenous male deaths and 39.5% of Indigenous female deaths in the 1991-96 intercensal period were estimated to be registered as such. These estimates were then applied across all age groups to obtain an adjusted number of Indigenous deaths which occurred during 1995-97. These estimated death numbers were then used in the construction of experimental abridged life tables.

Indigenous deaths are under-registered in all States/Territories, but with a high degree of variability. South Australia (SA), Western Australia (WA) and the Northern Territory (NT) had sufficient registration coverage in 1991-97 to provide enough Indigenous deaths to attempt estimates of life expectancy. Preston-Hill analysis indicates that SA, WA and the NT all had significantly higher coverage of Indigenous deaths than Australia overall.

At the national level, the life expectancy at birth in the period 1995-97 was estimated to be about 54 years for Indigenous males and 61 years for Indigenous females. However, life expectancy estimates derived from combining data from SA, WA and NT, the States/Territory with the best deaths coverage, are likely to be more reliable than the national estimate of Indigenous life expectancy. The combined data suggests life expectancy at birth of about 57 years for males and 63 years for females.

The estimates suggest life expectancy for each of SA, WA and NT are higher than the national estimates for both sexes. WA had the highest life expectancy at birthat around58 years for males and 64 years for females. SA and NT had similar life expectancies for both sexesat around 55 years for males and 63 years for females.

No life tables were produced for other States/Territories. During 1991-97, there were too few Indigenous deaths registered in Victoria, Tasmania and the Australian Capital Territory. Over the same period, the completeness of death registration was too low in New South Wales andQueensland.

The Preston-Hill method assumes that the completeness of enumeration and of death registration do not vary with age. These are unlikely to be true for theIndigenous population. The implications of these assumptions are that life expectancy is probably within 1-2 years of the estimates given. Furthermore, the analysis presented in this paper also assumes that 1995-97 deaths coverage is the same as 1991-96 deaths coverage. For that reason, the estimates of life expectancy for 1995-97 presented here are probably under-estimates.

1. INTRODUCTION AND AIM

Australia has a very good system of population measurement by international standards. There are accurate censuses of population and housing every five years, birth and death registration has high coverage, and all movements into and out of Australia are monitored. Therefore it is possible to maintain high quality estimates of the total Australian population. However, there are a range of data quality issues associated with estimating the Aboriginal and Torres Strait Islander (Indigenous) population.

The standard approach to calculating death rates relies on applying the number of deaths in a given period to the 'exposed to risk' population during that period. Without accurate data on Indigenous births and deaths, and accurate data on the size and structure of the Indigenous population, the standard method for calculating Indigenous death rates cannot be used.

This paper describes how a demographic technique outlined by Preston and Hill (1980) is used to estimate the completeness of Indigenous death registration and calculate death rates for the Indigenous population. It then shows how these rates are used to produce Indigenous life tables for Australia and selected States/Territories for 1995-97. Comparison with the 1991-96 experimental Indigenous life table and non-Indigenous mortality are made. Finally, the implications of the assumptions made in this analysis are discussed.

Before attempting to estimate the completeness of Indigenous death registration, it is important to recognise the major data quality issues relating to the Indigenous population.

Coverage of Indigenous births and deaths

While virtually all births and deaths are registered, not all Indigenous births and deaths are recorded as being Indigenous. The coverage of birth registrations is better than the coverage of death registrations. The total number of Indigenous births registered in Australia in 1998 was around 90% of the number of births projected in the 'low' series of the 1996-base experimental Indigenous population projections (ABS 1999b). By comparison, only about 61% of Indigenous deaths were registered in Australia in 1998 compared with the same population projection (ABS 1999c).

During 1995-97, 4,237 Indigenous deaths were identified as occurring in Australia (Table 1). The number of Indigenous deaths ranged from an average of almost 400 per year in Northern Territory (NT) and Western Australia (WA) to less than 10 per year in Tasmania and Australian Capital Territory. As well as the differences in number, there is a high degree of variability in the deaths coverage among States/Territories. Prior to 1998, only South Australia (SA), WA and NT had relatively high coverage. These States/Territory provide sufficient Indigenous deaths to attempt to produce estimates of life expectancy.

(a) Registered up to 1998(b)Only 20 deathswere registered as occurring in 1995.(c) Includes Other Territories

Coverage of Indigenous persons in the Census of Population and Housing

Indigenous people are more likely to be missed than the rest of the population by the census. The 1996 Post-Enumeration Survey (PES) estimated a net undercount of 7.1% for Indigenous persons and 1.5% for non-Indigenous persons (ABS 1998a). Taking this into account and other adjustments (ABS 1998a, p.23), the estimated resident Indigenous population at 6 August 1996 (census date) was 9.6% higher than the enumerated Indigenous population census count (i.e. 386,913 compared with 352,949, ).

Changing propensity to identify as Indigenous

Changes in the propensity of an individual to identify as being of Indigenous origin in the census is an important issue in considering the Indigenous population. The difference between the 1991 and 1996 census counts of Indigenous persons, as recorded on census forms, was significantly larger than expected, despite similar collection procedures for the two censuses. The number of people counted as Indigenous (including Other Territories) increased from 265,371 in the 1991 Census to 352,970 in the 1996 Census, an increase of 33%. Just under half of this increase was explainable from demographic factors such as births, deaths and migration (Ross 1999). Much of the remaining increase can be attributed to changes in the propensity of Indigenous people to identify as Indigenous on census forms (Ross 1999, ABS 1999a).

These issues impact on the size and age-sex structure of the Indigenous population and thus on the production of Indigenous life tables.

2. ESTIMATING THE COMPLETENESS OF DEATH REGISTRATION

2.1. PRESTON-HILL METHOD

In a population where net overseas migration is zero, the following relationship exists for age cohorts measured at two different points in time:

Pc2 = Pc1 - Dc

(1)

where:

Pc1 =

the true size of the population cohort c at time 1

Pc2 =

the true size of the population cohort c at time 2

Dc =

the number of deaths occurring for population cohort c, between time 1 and time 2.

Equation (1) describes an 'ideal' situation in which the population being studied is perfectly enumerated at time 1 and at time 2, and the number of deaths occurring between these times is also perfectly enumerated. In reality, this rarely occurs. Correction factors therefore need to be incorporated to compensate for under-enumeration when population counts are taken (i.e. under-enumeration in census counts) and under-registration of intercensal deaths. The equation then becomes:

YPc2 = XPc1 - ZDc

(2)

where:

X, Y, Z =

correction factors to adjust for under-enumeration in Pc1, Pc2 and Dc

Preston and Hill (1980) outlined a method which can be used to estimate the completeness of death registration. This method can cope with changes in the completeness of enumeration and omission of deaths from the death registration system at the same time. The method uses the linear relationship shown in equation (2). If deaths were the only cause of change in the size of a cohort (i.e. no migration and no change in census coverage/identification) then a cohort which experienced a certain death rate would decrease in size by the same amount. For example, a population experiencing a 2% death rate would fall by 2% in a year. The Preston-Hill method is based on this premise. A detailed discussion of the method can be found elsewhere (Cunningham and Paradies, 2000).

The basic data input for the Preston-Hill method is:

enumerated population at first census

enumerated population at second census

registered deaths during intercensal period to cohort of first census.

In a closed population, where the population is accurately measured and all deaths are registered and correctly attributed to the appropriate population age group, values of the inverse survival ratio between the censuses and apparent death rate for successive cohorts will lie on a straight line. The line can be expressed as:

SR-1 = 1d + 1

(3)

where:

SR-1 ==

inverse survival ratio between the censusesenumerated population at the first census ÷ enumerated population at the second census

d ==

apparent death rate at the end of the periodregistered intercensal deaths ÷ enumerated population at the second census.

In line (3), the intercept is equal to the completeness of enumeration of the first census relative to that of the second (in this case 1, meaning 100% complete) and slope is equal to the completeness of enumeration of the first census relative to that of intercensal death registration (in this case 1, meaning 100% complete). The intercept ÷ slope gives the completeness of intercensal death registration relative to the completeness of enumeration of the second census.

The method does not assume that perfect recording actually exists. On the contrary, it assumes that deaths are subject to under-coverage and it attempts to estimate the magnitude using observed data. This method, however, may not work well if the actual coverage is too low.

2.2 APPLICATION OF PRESTON-HILL METHOD TO INDIGENOUS DATA

To apply the Preston-Hill method to the 1991-96 period, the number of intercensal deaths occurring for each age cohort at the 1991 Census was estimated from data on age at death. This was derived from annual deaths registered with State Registrars. For example, to estimate the number ofintercensal deaths to persons aged 0 years at the 1991 Census, the following data was usedas a close approximation:

Year of death

Date of occurrence

Age (years)

1991

From 7 August to 31 December

0

1992

January to December

1

1993

January to December

2

1994

January to December

3

1995

January to December

4

1996

From 1 January to 6 August

5

Similarly, the intercensal deaths to persons aged 1 year, 2 years, 3 years up to 115+ years at the 1991 Census were obtained and then grouped into conventional five-year age groups(see Table A1 in Appendix1). The Preston-Hill method is applied to intercensal deathsusing five-year age cohorts, with a line of best fit determining the relationship between the inverse survival ratio between the censuses and the apparent death rate at the end of the period.

2.2.1 Survival ratios based on census counts and ERP

Census counts based survival ratios were calculated by dividing the 1991 Census counts by the 1996 Census countsof each age-sex cohort. Similarly, ERP based survival ratios were calculated by dividing the 1991 ERP (1996 Census based) by the 1996 ERP. As discussed further in 2.2.2, survival ratios were able to be calculatedfor Australia, SA, WA, NT, as well asSA, WA and NT combined(Table 2). Only survival ratios for cohorts up to age 70+ years in 1991 are able to be presented, as the Indigenousestimated resident population (ERP) was only generated up to age 75+ years in 1996.

A survival ratio cannot have a value greater than 1 if the Indigenous population is perfectly enumerated in both censuses. Quite a few of the male and female census-based survival ratios are greater than 1, meaning that there were more survivors in those age cohorts in 1996 than in 1991. None of the ERP-based survival ratios are greater than 1. For this reason, ERP rather than census counts were preferred in our Preston-Hill analysis to estimate the completeness of Indigenous death registration.

ERP-based survival ratios for the 70+ age group were alsoconsiderably lower than those for other age groups. This suggests a possiblebias in age reporting or higher rates of mis-identification in the older age groups, either deliberate or accidental. Because of this particular unreliability in older age groups, Preston-Hill analysis was conducted without this upper age group which otherwise lowered confidence in the regression curve.

2.2.2. Completeness of Indigenous death registration

To estimate the completeness of Indigenous death registration in Australia, the 1991 and 1996 experimental estimates of Indigenous population and all Indigenous deaths occurring (and registered)in Australia between the1991 and 1996 Censuses were used in Preston-Hill analysis. Figure 1 shows the relationship between the inverse survival ratio (i.e. 1 ÷ survival ratio) and apparent death rate for Indigenous males and females. The method suggests that only 39.1% (= intercept ÷ slope = 0.9985 ÷ 2.5519), or 2 in every 5 Indigenous male deaths occurring in Australia between the 1991 and 1996 Censuses were registered as such. The corresponding figure for Indigenous females was 39.5%. In constructing Indigenous life tables for Australia, this is the factor by which observed death rates were inflated to equal true death rates. The use of cumulated data, starting with successive initial cohorts aged 0+, 5+, 10+, and so on, produces similar coverage estimates to those presentedhere.

The same coverage factor (39.1% for males and 39.5% for females) is used across all age groups to calculate adjusted death rates. In doing so, the Preston-Hill method assumes that the completeness of censusenumeration and death registration does not vary with age. This is unlikely to be the case for Indigenous population. The implications of these assumptions are discussed in this paper in 'Implications of assumptions'.

Table 3 shows the estimates of proportions of Indigenous deaths registered in Australia and its States/Territories. Because of the small number of Indigenous deaths registered as occurring during 1991-96 in Victoria, Queensland, Tasmania and Australian Capital Territory, completeness of death registration could not be calculated for these jurisdictions.

(a) Based on deaths registered up to 1998 that occurred in the 1991-96 intercensal period.(b) Based on deaths registered in the 1992-96 calendar years compared with deaths projected from the 1992-96 experimental Indigenous population estimates (1996 Census based).

There exists a high degree of variability in the completeness of Indigenous deaths among the States/Territories. Coverage estimates are very low for New South Wales (NSW): 30% for males and 26% for females. Because of this low coverage and the small number of deaths registered as occurred in NSW during 1995-97, no life table has been produced for NSW. SA, WA and NT had significantly higher coverage of Indigenous deaths than Australia as a whole. NT had the highest coverage (male deaths 90%, female deaths 95%), followed by WA (male deaths 86%, female deaths 90%). These estimates are obtained from Preston-Hill analysis and are used to obtain adjusted death rates.

The coverage estimates presented above are different to those presented elsewhere. In ABS (1999c), coverage estimates are calculated by dividing the number of deaths registered by the number of deaths projected from the 1996 Census-based experimental projections('low' series). To facilitate comparison, these estimates are also shown in Table 3. The estimates derived from Preston-Hill analysis are based on registered deaths that occurred in the1991-96 intercensal period, whereas the estimates obtained using registered and projected deaths are based on 1992-96 death registrations. The coverage estimates based on the projected deaths are somewhat lower than those obtained from the Preston-Hill analysis (Table 3). This is because projected deaths were derived using mortality levels based on 1991-96 Indigenous life tables, which produced lower mortality than the experimental 1995-97 life tables.

3. INDIGENOUS ABRIDGED LIFE TABLES

Abridged life tables are generally constructed in preference to complete life tables when reliable age-specific death rates are not available by single years of age. Reliable single year age-specific deaths rates are not available for the Indigenous population. However, abridged life tables are generally sufficient for most purposes of demographic analysis.

In constructing 1995-97 experimental Indigenous abridged life tables, mortality rates based on 1995-97 data were used. Mortality rates were calculated by dividing the average annual number of deaths occurring during 1995-97 by the experimental Indigenous ERP at June 1996. Deaths were averaged over this three-year period to smooth out the irregularities from year to year in the number of deaths, bearing in mind the relatively small number of Indigenous deaths in many areas and age groups. Deaths were centred on the 1996 mid-year population estimate, which was based on 1996 Census counts. A general discussion of life tables, various functions and details of mortality calculations are given in the Appendix 2.

Five separate life tables have been produced: one for Australia; one each for SA, WA and NT; and another for SA, WA and NT combined. The all-Australia life table was produced by using all Indigenous deaths that had been registered up to 1998 thatoccurred in Australia during 1995-97. Each State/Territory life table was based on deaths that occurred to residents of that particular jurisdiction. The SA, WA and NT combined life table used deaths that occurred to residents of these three jurisdictions combined. All these life tables are presented in Appendix 4.

Table 4 presents the observed and adjusted life expectancies for Australia, SA, WA, NT and SA, WA and NT combined. The observed life expectancies are based on the actual number of deaths which are not adjusted for undercoverage. There is undercoverage of Indigenous deaths to some degree in all States/Territories. As a result, the observed life expectancies are over-estimates of the true life expectancies. The adjusted life expectancies, on the other hand, are based on the number of deaths which are obtained after inflating the observed number of deaths by the Preston-Hill under-coverage factor and hence are expected to be closer to reality than the observed life expectancies.

At the national level, the adjusted life expectancy at birth in the period 1995-97 was estimated to be about 54 years for Indigenous males and 61 years for Indigenous females. SA and NT have similar adjusted life expectancies for both sexes. The life expectancies for WA are only slightly higher than those for SA and NT. Australian life expectancy estimates are lower than these State-specific estimates. Male life expectancy based on SA, WA and NT combined data is 3 years higher than that of the national estimate. The female life expectancy of these three States/Territory combined, on the other hand, is only 1 year higher than that of the national estimate. These combined estimates, as based on data of the States/Territory with the best coverage, are thought to be more reliable than the national estimates.

Indigenous males experience higher mortality than Indigenous females at all ages of life (Figure 2). Both male and female mortality rates commence with relatively high infant mortality. The rate falls rapidly to its lowest between ages 5-9: the chance of dying at these ages is lower than at any other age. The gap between male and female mortality is greatest in the young adult ages (15-24 years), with males more prone to accidental deaths and suicide.

There are marked mortality differences between Indigenous Australians and total Australians (Figure 3). Total Australian males and females experience significantly lower mortality than their Indigenous counterparts at all ages of life. Both total and Indigenous male mortality show a steep rise during the teenage years, primarily associated with motor vehicle accidents and suicide.

At the national level, the life expectancy at birth of Indigenous males in 1995-97 was estimated to be 54.1 years (Table 4). This compares to the life expectancy of Indigenous males of 56.9 years previously estimated for 1991-96 (ABS 1999c), a decrease of 2.8 years (Table 5). The life expectancy at birth of Indigenous females in the 1995-97 period was estimated to be 61.3 years, 0.3 years less than that in 1991-96. What is the reason for the apparent decrease in Indigenous life expectancy? It could be due to improved recording of Indigenous deaths, particularly male deaths, including the introduction of a question on Indigenous status on Queensland death registration forms in 1996. It could also be due to the differences in methodology used. In estimating the completeness of Indigenous death registration, Indigenous ERP has been used for 1995-97 whereas the 1991-96 life table used Indigenous census counts. For these reasons, comparison of life expectancy estimates presented in this paper with estimates from other sources should only be undertaken with extreme caution. The lower life expectancy at birth in 1995-97 than in 1991-96 does not necessarily mean that the Indigenous mortality has declined during this period.

In general, Indigenous male mortality is higher in the experimental 1995-97 life tables than in 1991-96 for all age groups (Table 5 and Figure 4). Conversely, Indigenous female mortality is lower for most age groups in the 1995-97 life table. The degree of change, however, varies with age. The greatest percentage change is observed in ages 20-54 years.

Both male and female life expectancy estimates in the period 1995-97 based on SA, WA and NT combined data are higher than the national estimates (Table 4). This result is inconsistent with that of a previous investigation where separate Indigenous experimental life tables for western (SA, WA and NT combined) and eastern (rest of the five States/Territories combined) parts of Australia have been produced. Although the life tables themselves have not been published, the resulting estimates of life expectancy at birth have been published (ABS, 1999a; Cunningham and Paradies, 2000) and reported that in 1991-96, the combined estimates of the three western States/Territories are lower than the Australian estimates. This inconsistency could also be due to the reasons mentioned above.

4. COMPARISON BETWEEN INDIGENOUS AND NON-INDIGENOUS POPULATION

4.1 LIFE EXPECTANCY

The life expectancy at birth for the Indigenous population differs greatly from that of the total Australian population. Indigenous males in 1995-97 are expected to live 54 years, around 21.5 years less than life expectancy for total males (75.7 years), while Indigenous females are expected to live 61 years, around 20 years less than the life expectancy for total females (81.4 years). The difference in life expectancy between Indigenous and total Australian populations, stems from the difference in age-specific death rates between the Indigenous and non-Indigenous populations.

4.2 STANDARDISED DEATH RATES

Death is strongly related to age. The age structure of the Indigenous population is very different to that of the non-Indigenous population. At June 1996, Australia's Indigenous population had a median age of 20 years, about 14 years younger than that of the total population (ABS 1998a). To compare the death rates of these vastly different populations, it is important to take this age difference into account. One way of adjusting for differences in age distributions is to calculate standardised death rates.

Standardised death rates for Indigenous and non-Indigenous males and females (Table 6) are calculated by deriving age-specific death rates and applying these to a standard population. The June 1991 total Australian ERP is used here as the standard population.

(a) Number of deaths per 1,000 population.(b) The crude death rate that would have prevailed if the total Australian estimated resident population at June 1991 had experienced at each age-sex the death rates of the respective Indigenous/non-Indigenous population.

Crude death rates for Indigenous males and females are much lower than for non-Indigenous males and females. This reflects the younger age structure of the Indigenous population. Standardised death rates, on the other hand, are higher for Indigenous males and females. The reason for higher standardised death rates for Indigenous people is that their age-specific death rates are higher than for their non-Indigenous counterparts at all ages (see Table A3 in Appendix 3). This is further support for the Indigenous population having lower life expectancy (at all ages) than the non-Indigenous population.

4.3 MEDIAN AGE AT DEATH

Half of the population dying are younger than the median age at death (and half are older). Median age at death represents another measure of relative mortality. A population with high life expectancy would be expected to have higher median age at death than another population with lower life expectancy, other factors being equal.

The non-Indigenous population has a markedly higher median age at death than the Indigenous population (Table 7). In 1998, a difference of over 26 years was observed between the median age at death of the Indigenous and non-Indigenous population. Females die older than males, on average. Over the period 1991-98, there was some fluctuation in median age at death. Median age at death for Indigenous males was 0.5 year higher in 1995-97 than in 1991-96. It might be affected by the improved recording of Indigenous male deaths. The median age at death for Indigenous females, however, declined 0.4 year between these two overlapping periods. For the non-Indigenous population, it increased from 76.6 years in 1991-96 to 77.1 years in 1995-97.

Table 7: MEDIAN AGE AT DEATH (YEARS), By Indigenous Status, Sex and Year of Registration,
Australia, 1991-98

Year

Period

Indigenous Status by Sex

1991

1992

1993

1994

1995

1996

1997

1998

1991-96

1995-97

Indigenous males

46.2

49.7

47.7

48.3

48.6

47.9

49.8

47.7

48.4

48.9

Indigenous females

55.5

56.8

57.4

59.7

57.6

57.7

56.8

57.0

57.6

57.2

Indigenous persons

49.7

52.8

51.9

52.5

52.3

52.0

52.4

51.3

52.4

52.3

Non-Indigenous males

72.3

72.7

73.0

73.6

73.6

74.2

74.4

74.7

73.5

74.1

Non-Indigenous females

78.9

79.4

79.6

80.2

80.4

80.8

81.1

81.2

80.1

80.8

Non-Indigenous persons

75.5

76.0

76.2

76.7

76.8

77.2

77.4

77.6

76.6

77.1

Total males

72.2

72.6

72.9

73.5

73.5

74.0

74.2

74.5

73.5

74.1

Total females

78.8

79.3

79.5

80.2

80.3

80.7

81.0

81.0

80.1

80.8

Total persons

75.4

75.9

76.1

76.6

76.6

77.0

77.2

77.4

76.6

77.1

There is a high degree of variability in the Indigenous median age at death among the States/Territories (Table 8). SA, WA and NT have the best coverage and consistently highest registrations of Indigenous deaths, so their median ages are likely to be more reliable than for other States/Territories. The relative median age at death in each State/Territory is consistent with the relative estimated life expectancy (Table 4) in each State/Territory. That means that if the median age at death of a State/Territory is high (low), its life expectancy is also high (low). For instance, among SA, WA and NT, WA has the highest median age at death (Table 8) and also the highest life expectancy at birth (Table 4). This is true for both males and females.

Table 8: MEDIAN AGE AT DEATH (YEARS), Indigenous Population, By Sex, Period of Registration and State/Territory, 1991-97

Male

Female

Total

State/Territory

1991-96

1995-97

1991-96

1995-97

1991-96

1995-97

NSW

48.4

48.8

59.1

59.4

52.8

53.9

Vic

47.3

48.7

60.0

64.7

52.3

56.3

Qld

49.3

50.3

59.0

58.2

53.2

53.4

SA

45.8

47.0

52.7

52.8

49.0

49.6

WA

50.3

48.8

60.1

58.3

54.9

53.0

Tas

49.5

38.8

37.5

65.0

49.0

49.5

NT

48.0

48.5

55.1

53.8

50.6

50.5

ACT

47.5

50.0

73.0

54.0

50.5

50.0

SA, WA and NT combined

48.5

48.4

57.2

55.4

52.2

51.2

Australia

48.4

48.9

57.6

57.2

52.4

52.3

5. IMPLICATIONS OF ASSUMPTIONS

This paper carried out an investigation into the production of Indigenous life tables for 1995-97 using a demographic technique outlined by Preston and Hill (1980). The Preston-Hill method is based on a number of assumptions including a closed population; that the completeness of enumeration and death registration are both constant across age; correct reporting of age in censuses and death registrations; and stable mortality during the intercensal period. The implications of these assumptions are discussed below.

Migration

Census data indicate that the in-migration rate of the Indigenous people is very low (ABS 1998b). The out-migration rate can be assumed to be similarly very low. The experimental Indigenous population projections assumed nil overseas migration (ABS 1998b). Although the levels of net interstate movement are more significant, interstate migration during 1991-97 should not significantly influence the results of this Preston-Hill analysis.

Changing propensity to identify as Indigenous

The issue of changes in the propensity of an individual to identify as being of Indigenous origin in the census deserves attention. The calculation of the completeness of coverage of Indigenous deaths by the Preston-Hill method assumes that the observed count at the 1996 Census is complete, which means that changes between 1991 and 1996 in the propensity of people to identify as Indigenous on census forms are taken into account.

Completeness of enumeration

The Preston-Hill method assumes that the completeness of enumeration does not vary with age. This is unlikely to be the case for the Indigenous population, given the experience of census under-enumeration. In the 1996 Census, young adult males among the Australian population had the highest undercount rate, with 4.3% for males aged 20-24 and 3.7% for males aged 25-29 compared with 1.6% average across the total Australian population (ABS 1997a). Such age-specific undercount rates were not available for the Indigenous population, but when estimating the experimental Indigenous population it was assumed that the enumeration of Indigenous population also varied considerably with age.

For simplicity in the Preston-Hill method, it is assumed that both the 1991 and 1996 Censuses had the same pattern of under-enumeration. In other words, the age pattern of undercount is assumed to be the same in 1991 and 1996. In that case, both the numerator and denominator of the inverse survival ratio, which is used in this analysis to estimate the coverage of death registration, will be subject to equal proportionate errors. The estimates of the proportion of deaths registered obtained using Preston-Hill analysis and hence the life expectancy estimates will therefore remain unchanged.

Coverage of death registration

The method also assumes that the coverage of death registration is the same across all ages. Following this assumption, the same coverage factor (0.391 for males and 0.395 for females) is used across all age groups to obtain adjusted death rates. This is unlikely to apply to the Indigenous population. Will the resultant life expectancy estimates be changed substantially if differential coverage factors are used? To examine this, some differential coverage factors are presented in Table 9.

Scenario 1 represents the undercoverage factors used in the 1995-97 draft experimental life table for Australia (Table A4 in Appendix 4).

In Scenario 2, for example, the male coverage factor for age groups 0-19 and 60+ years has been increased from 0.39 to 0.59. But coverage for age group 20-59 years has been decreased from 0.39 to 0.31 to offset the increase in the other age groups. This keeps the total number of deaths roughly the same and the overall coverage rate at about 0.39. Scenarios 3 and 4 represent alternative differential age inflation factors. The three broad age groups have been arbitrarily chosen, although they do approximate young dependents (0-19 years), the main working ages (20-59 years) and older dependents (60+ years). It could be argued that dependent age groups may or may not be more likely to be identified as Indigenous when they die.

This sensitivity analysis show that life expectancy would be lower by 1.2 year for males and 1.0 years for females if the coverage among the youngest and oldest age groups was increased by 40% (i.e. from Scenario 1 to Scenario 3), with an offsetting decrease in coverage in the middle age group. This suggests that even if the actual coverage of Indigenous deaths is substantially different from those used here, it is unlikely to have a major impact on life expectancy.

1991-96 coverage compared with 1995-97 coverage

The analysis presented in this paper also assumes that the 1995-97 Indigenous deaths coverage is the same as the 1991-96 coverage. This is probably not true for the Indigenous population. For example, coverage estimates in ABS (1999c) suggest that 1997 death coverage is higher than 1996 coverage. Scenarios 5 and 6 (Table 9) illustrate the effect of increasing overall death coverage from 0.39 to 0.45 and 0.50, respectively. If death coverage is higher, then the adjustment needed to registered deaths is smaller. If the Indigenous death coverage was as high as 0.50 in 1995-97, male life expectancy at birth would be higher by 3.6 years (from 54.1 years in Scenario 1 to 57.7 years in Scenario 6) and female life expectancy by 3.3 years (from 61.3 years in Scenario 1 to 64.6 years in Scenario 6).

Correct reporting of age

Correct reporting of age is important to ensure that both population and deaths are correctly included in the appropriate age cohort. A systematic overstatement of age in censuses or in death registrations will result in an overestimate of the completeness of death registrations (Preston and Hill 1980). To minimise the effect of age overstatement, the fitting of Preston-Hill curves was conducted by excluding ages 70+.

Stable mortality during the intercensal period

The assumption that there are insignificant changes in mortality during the intercensal period is reasonable, but it is impossible to differentiate and quantify changes in mortality over time from improvement in the level of Indigenous identification (in both death registration and census enumeration).

6. CONCLUSION

The life expectancy estimates presented in this paper are described as experimental because of the nature of the base population, which is affected by the intercensal volatility in the counts of the Indigenous population, and deficiencies in deaths and births registration data. Consequently, there is uncertainty about the accuracy of death rates which use census counts or census-based population estimates as their denominator. The life expectancy estimates are therefore sensitive to the inputs used and over-precise analysis is cautioned. They should be used only as an indicative summary measure of the level of mortality of the Indigenous population.

(a) Registered up to 1998 that occurred in the 1991-96 intercensal period.

APPENDIX 2: THE LIFE TABLE

INTRODUCTION

A life table is a useful demographic tool for combining and summarising mortality rates of a population at different ages into a single statistical model. In its simplest form, a life table is generated from age-specific mortality rates and the resulting values are used to measure mortality, survivorship and life expectancy.

The life table describes the mortality experience of a hypothetical group of new born babies throughout their entire lifetime. It is based on the assumption that this group is subject to the age-specific mortality rates of the reference period. Typically this hypothetical group is 100,000 in size. A life table population is therefore the population which would exist if the age-specific death rates prevailing at some particular time were to continue throughout the life span of all the individuals, with no change in the number of births each year and no migration.

Life tables may be complete or abridged, depending on the age interval used in their compilation. Complete life tables contain data for single years of age, while abridged life tables usually contain data for five-year age groups.

Life expectancy refers to the average number of additional years a person of a given age and sex might expect to live if the age-specific death rates of the given period continued through their lifetime. The life expectancy at birth is used as an index of the level of mortality prevailing in a community in a given period. It represents the average number of years a new born baby could expect to live if the mortality rates of today were to continue through that baby's life.

LIFE TABLE FUNCTIONS

Abridged life tables for the Indigenous population contain the following life table functions:

nmx = Adjusted age-specific mortality rate for persons aged x to x + n;nqx = Proportion of persons dying between exact age x and exact age x + n;lx = Number of persons surviving at exact age x;ndx = Number of deaths between exact age x and exact age x + n;nLx = Number of persons-years lived during the interval age x to age x + n;Tx = Total number of person-years that would be lived after exact age x; andex = Complete expectation of life at exact age x.

The principal step in life table construction is one of calculating age-specific mortality rates or probability of dying. Below is a discussion of how mortality rates at different ages are calculated.

CALCULATION OF INFANT MORTALITY (1q0)

The infant mortality rate is usually defined as the number of infant deaths per 1,000 live births in a particular year. However, this rate is not a true probability as the denominator (births during the year) does not represent the initial population 'exposed to risk' (Shyrock and Siegel). Some infant deaths occurring during any given year will be to infants born in the previous year. Therefore, in calculating infant mortality rate, appropriate separation factors are used to relate deaths occurred in a given year to infants born in the same year. Table A2 illustrates the calculation of infant mortality rates for Indigenous males and females for the period 1995-97

(1) Based on the estimated proportion of Indigenous deaths registered obtained from Preston-Hill analysis (0.395 for males and 0.391 for females).

where:

Dy = the registered number of deaths occurring in year yBy = the registered number of births occurring in year yBy-1 = the registered number of births occurring in year y-1D'y = the registered number of deaths occurring in year y to births in year yD"y= the registered number of deaths occurring in year y to births in year y-1f' = the proportion of deaths occurring in year y to births in year yf" = the proportion of deaths occurring in year y to births in year y-1

Value of nqx for infants (1q0) were calculated using the following equation:

1q0 = Dy / (f'By + f"By-1)

(5)

The 1q0 obtained in equation (5) was then divided by the estimate of proportions of deaths registered derived from Preston-Hill analysis.

The calculation of infant mortality rate can be better explained by the following example. For y = 1996 we have from Table A2:

By =

4,874

Dy =

D'y + D"y = 54 + 12 = 66

By-1 =

3,458

f' =

D'y / (D'y + D"y) = 54/(54 + 12) = 0.815

f" =

1 - f' = 0.185

Therefore the infant mortality rate for Indigenous males for the year 1996 was calculated as 1000* Dy / (f'By + f"By-1) = 14.30. The corresponding figures for 1995 and 1997 were 13.11 and 13.31 respectively giving an average infant mortality rate of 13.57 for the period 1995-97. The average infant mortality rate was then divided by the proportion of deaths registered according to Preston-Hill analysis to get an adjusted rate.

The estimates of adjusted infant mortality rates were found to be 35 per 1,000 live births for Indigenous males and 32 per 1,000 live births for Indigenous females.

ESTIMATION OF MORTALITY AT AGES 1-74

Mortality rates (nqx values) for persons aged 1-74 were derived from central death rates (nmx values). These nmx values were calculated for the period 1995-97 using the following equation:

nmx =( nDx95 + nDx96 + nDx97)/(3 * nPxC)

(6)

Where:

nmx = the central death rate for persons aged x to x + n

nDx = registered deaths occurring during the year to persons aged x to x + n

nPx = the estimated Indigenous population at 30 June 1996

The nmx values were then divided by the estimated proportions of deaths registered obtained from Preston-Hill analysis to derive the adjusted nmx values.

nqx values were derived from adjusted nmx values as follows:

nqx = n * nmx/(1 + (n/2 * nmx))

(7)

ESTIMATION OF MORTALITY AT AGES 75+

Since all persons aged 75 and over will die while still within this age group, the probability of dying after age 75 is 1.

ESTIMATION OF lx, nLx, Tx AND e0x

The value for l0 (the radix) is set at 100,000. Remaining values of lx are calculated as:

(a) Based on Indigenous deaths registered up to 1998 that occurred in 1995-97 and experimental Indigenous estimated resident population at 30 June 1996.(b) Based on non-Indigenous deaths registered up to 1998 that occurred in 1995-97 and total Australian estimated resident population less experimental Indigenous estimated resident population at 30 June 1996.

nmx = Adjusted age-specific death rate for persons aged x to x + nnqx = Proportion of persons dying between exact age x and exact age x + nlx = Number of persons surviving at exact age xnLx = Number of persons-years lived during the interval age x to age x + nTx = Total number of person-years that would be lived after exact age xe0x = Complete expectation of life at exact age x

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